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Simplifying 14400 = -16t2 + 1600t Reorder the terms: 14400 = 1600t + -16t2 Solving 14400 = 1600t + -16t2 Solving for variable 't'. Reorder the terms: 14400 + -1600t + 16t2 = 1600t + -1600t + -16t2 + 16t2 Combine like terms: 1600t + -1600t = 0 14400 + -1600t + 16t2 = 0 + -16t2 + 16t2 14400 + -1600t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 14400 + -1600t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(900 + -100t + t2) = 0 Factor a trinomial. 16((10 + -1t)(90 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Subproblem 2
Set the factor '(90 + -1t)' equal to zero and attempt to solve: Simplifying 90 + -1t = 0 Solving 90 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + -1t = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -1t = 0 + -90 -1t = 0 + -90 Combine like terms: 0 + -90 = -90 -1t = -90 Divide each side by '-1'. t = 90 Simplifying t = 90Solution
t = {10, 90}
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